Coordinate AlgebraDay 75

•Warm-Ups• Transformations GO• Review• Comparing Functions Notes

Unit 3 ReviewLearning Targets:Students can identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior.

Domain & Range

Domain:

Range:

3 4x

2 4y

Domain & Range

Domain:

Range:

Increasing or decreasing?

x

y

Domain & Range

Domain:

Range:

Increasing or decreasing?

x

4 y

Domain & Range

Domain:

Range:

Increasing or decreasing?

x

0y

Operations with Functions

Find 2f(x) + 3g(x)

Find g(x) – f(x)

Find f(-3)

2 2( ) 2 5 11 and ( ) 4 4 5f x x x g x x x

Increasing and Decreasing

Increasing:

Decreasing:

Constant:

2,3

3, 2

2,2

Comparing Functions

Learning Targets:Students can compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Comparing Functions

You MUST write a sentence comparing the two things.

Just because you can do the math does not

mean you understand it.

Comparing is showing understanding.

Comparing Intercepts

• When you compare y-intercepts, you are comparing start points.

• Just make a note of which function starts at a higher/lower value.

• When you compare x-intercepts, you are comparing where they hit the x-axis.

Comparing Rate of Change

• When comparing two linears, you can just compare their slopes.

• When comparing two exponentials or comparing an exponential and a linear, you will have to find the rate of change for a given interval and then compare.